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Language	Haskell2010

Numeric.Optimization.Algorithms.HagerZhang05.AD

Contents

Main function
Result and statistics
Options
Technical parameters
Re-export

Synopsis

optimize :: forall f. Traversable f => Parameters -> Double -> f Double -> (forall s. Reifies s Tape => f (Reverse s Double) -> Reverse s Double) -> IO (f Double, Result, Statistics)
data Result
- = ToleranceStatisfied
- | FunctionChange
- | MaxTotalIter
- | NegativeSlope
- | MaxSecantIter
- | NotDescent
- | LineSearchFailsInitial
- | LineSearchFailsBisection
- | LineSearchFailsUpdate
- | DebugTol
- | FunctionValueNaN
- | StartFunctionValueNaN
data Statistics = Statistics {
- finalValue :: Double
- gradNorm :: Double
- totalIters :: CInt
- funcEvals :: CInt
- gradEvals :: CInt
}
defaultParameters :: Parameters
data Parameters = Parameters {
- printFinal :: Bool
- printParams :: Bool
- verbose :: Verbose
- lineSearch :: LineSearch
- qdecay :: Double
- stopRules :: StopRules
- estimateError :: EstimateError
- quadraticStep :: Maybe Double
- debugTol :: Maybe Double
- initialStep :: Maybe Double
- maxItersFac :: Double
- nexpand :: CInt
- nsecant :: CInt
- restartFac :: Double
- funcEpsilon :: Double
- nanRho :: Double
- techParameters :: TechParameters
}
data Verbose
- = Quiet
- | Verbose
- | VeryVerbose
data LineSearch
- = ApproximateWolfe
- | AutoSwitch Double
data StopRules
- = DefaultStopRule Double
- | AlternativeStopRule
data EstimateError
- = AbsoluteEpsilon Double
- | RelativeEpsilon Double
data TechParameters = TechParameters {
- techDelta :: Double
- techSigma :: Double
- techGamma :: Double
- techRho :: Double
- techEta :: Double
- techPsi0 :: Double
- techPsi1 :: Double
- techPsi2 :: Double
}
class (Num t, Num (Scalar t)) => Mode t where
- type Scalar t :: Type
- auto :: Scalar t -> t

Main function

optimize Source #

Arguments

:: Traversable f
=> Parameters	How should we optimize.
-> Double	`grad_tol`, see `stopRules`.
-> f Double	Initial guess.
-> (forall s. Reifies s Tape => f (Reverse s Double) -> Reverse s Double)	Function to be minimized.
-> IO (f Double, Result, Statistics)

Run the CG_DESCENT optimizer and try to minimize the function.

It uses reverse mode automatic differentiation to compute the gradient.

Result and statistics

data Result #

Constructors

ToleranceStatisfied	Convergence tolerance was satisfied.
FunctionChange	Change in function value was less than `funcEpsilon * \|f\|`.
MaxTotalIter	Total iterations exceeded `maxItersFac * n`.
NegativeSlope	Slope was always negative in line search.
MaxSecantIter	Number of secant iterations exceed nsecant.
NotDescent	Search direction not a descent direction.
LineSearchFailsInitial	Line search fails in initial interval.
LineSearchFailsBisection	Line search fails during bisection.
LineSearchFailsUpdate	Line search fails during interval update.
DebugTol	Debug tolerance was on and the test failed (see `debugTol`).
FunctionValueNaN	Function value became `NaN`.
StartFunctionValueNaN	Initial function value was `NaN`.

Instances

Enum Result
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods succ :: Result -> Result # pred :: Result -> Result # toEnum :: Int -> Result # fromEnum :: Result -> Int # enumFrom :: Result -> [Result] # enumFromThen :: Result -> Result -> [Result] # enumFromTo :: Result -> Result -> [Result] # enumFromThenTo :: Result -> Result -> Result -> [Result] #
Eq Result
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: Result -> Result -> Bool # (/=) :: Result -> Result -> Bool #
Ord Result
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: Result -> Result -> Ordering # (<) :: Result -> Result -> Bool # (<=) :: Result -> Result -> Bool # (>) :: Result -> Result -> Bool # (>=) :: Result -> Result -> Bool # max :: Result -> Result -> Result # min :: Result -> Result -> Result #
Read Result
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS Result # readList :: ReadS [Result] # readPrec :: ReadPrec Result # readListPrec :: ReadPrec [Result] #
Show Result
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> Result -> ShowS # show :: Result -> String # showList :: [Result] -> ShowS #

data Statistics #

Statistics given after the process finishes.

Constructors

Statistics
Fields finalValue :: Double Value of the function at the solution. gradNorm :: Double Maximum absolute component of the gradient at the solution. totalIters :: CInt Total number of iterations. funcEvals :: CInt Total number of function evaluations. gradEvals :: CInt Total number of gradient evaluations.

Instances

Eq Statistics
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: Statistics -> Statistics -> Bool # (/=) :: Statistics -> Statistics -> Bool #
Ord Statistics
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: Statistics -> Statistics -> Ordering # (<) :: Statistics -> Statistics -> Bool # (<=) :: Statistics -> Statistics -> Bool # (>) :: Statistics -> Statistics -> Bool # (>=) :: Statistics -> Statistics -> Bool # max :: Statistics -> Statistics -> Statistics # min :: Statistics -> Statistics -> Statistics #
Read Statistics
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS Statistics # readList :: ReadS [Statistics] # readPrec :: ReadPrec Statistics # readListPrec :: ReadPrec [Statistics] #
Show Statistics
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> Statistics -> ShowS # show :: Statistics -> String # showList :: [Statistics] -> ShowS #
Storable Statistics
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods sizeOf :: Statistics -> Int # alignment :: Statistics -> Int # peekElemOff :: Ptr Statistics -> Int -> IO Statistics # pokeElemOff :: Ptr Statistics -> Int -> Statistics -> IO () # peekByteOff :: Ptr b -> Int -> IO Statistics # pokeByteOff :: Ptr b -> Int -> Statistics -> IO () # peek :: Ptr Statistics -> IO Statistics # poke :: Ptr Statistics -> Statistics -> IO () #

Options

defaultParameters :: Parameters #

Default parameters. See the documentation for Parameters and TechParameters to see what are the defaults.

data Parameters #

Parameters given to the optimizer.

Constructors

Parameters

Fields

printFinal :: Bool
Print final statistics to stdout. Defaults to True.
printParams :: Bool
Print parameters to stdout before starting. Defaults to False
verbose :: Verbose
How verbose we should be while computing. Everything is printed to stdout. Defaults to Quiet.
lineSearch :: LineSearch
What kind of line search should be used. Defaults to AutoSwitch 1e-3.
qdecay :: Double
Factor in [0, 1] used to compute average cost magnitude C_k as follows:
```
Q_k = 1 + (qdecay)Q_{k-1},   Q_0 = 0
C_k = C_{k-1} + (|f_k| - C_{k-1})/Q_k
```
Defaults to 0.7.
stopRules :: StopRules
Stop rules that define when the iterations should end. Defaults to DefaultStopRule 0.
estimateError :: EstimateError
How to calculate the estimated error in the function value. Defaults to RelativeEpsilon 1e-6.
quadraticStep :: Maybe Double
When to attempt quadratic interpolation in line search. If Nothing then never try a quadratic interpolation step. If Just cutoff, then attemp quadratic interpolation in line search when |f_{k+1} - f_k| / f_k <= cutoff. Defaults to Just 1e-12.
debugTol :: Maybe Double
If Just tol, then always check that f_{k+1} - f_k <= tol * C_k. Otherwise, if Nothing then no checking of function values is done. Defaults to Nothing.
initialStep :: Maybe Double
If Just step, then use step as the initial step of the line search. Otherwise, if Nothing then the initial step is programatically calculated. Defaults to Nothing.
maxItersFac :: Double
Defines the maximum number of iterations. The process is aborted when maxItersFac * n iterations are done, where n is the number of dimensions. Defaults to infinity.
nexpand :: CInt
Maximum number of times the bracketing interval grows or shrinks in the line search. Defaults to 50.
nsecant :: CInt
Maximum number of secant iterations in line search. Defaults to 50.
restartFac :: Double
Restart the conjugate gradient method after restartFac * n iterations. Defaults to 1.
funcEpsilon :: Double
Stop when -alpha * dphi0, the estimated change in function value, is less than funcEpsilon * |f|. Defaults to 0.
nanRho :: Double
After encountering NaN while calculating the step length, growth factor when searching for a bracketing interval. Defaults to 1.3.
techParameters :: TechParameters
Technical parameters which you probably should not touch.

Instances

Eq Parameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: Parameters -> Parameters -> Bool # (/=) :: Parameters -> Parameters -> Bool #
Ord Parameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: Parameters -> Parameters -> Ordering # (<) :: Parameters -> Parameters -> Bool # (<=) :: Parameters -> Parameters -> Bool # (>) :: Parameters -> Parameters -> Bool # (>=) :: Parameters -> Parameters -> Bool # max :: Parameters -> Parameters -> Parameters # min :: Parameters -> Parameters -> Parameters #
Read Parameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS Parameters # readList :: ReadS [Parameters] # readPrec :: ReadPrec Parameters # readListPrec :: ReadPrec [Parameters] #
Show Parameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> Parameters -> ShowS # show :: Parameters -> String # showList :: [Parameters] -> ShowS #
Storable Parameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods sizeOf :: Parameters -> Int # alignment :: Parameters -> Int # peekElemOff :: Ptr Parameters -> Int -> IO Parameters # pokeElemOff :: Ptr Parameters -> Int -> Parameters -> IO () # peekByteOff :: Ptr b -> Int -> IO Parameters # pokeByteOff :: Ptr b -> Int -> Parameters -> IO () # peek :: Ptr Parameters -> IO Parameters # poke :: Ptr Parameters -> Parameters -> IO () #

data Verbose #

How verbose we should be.

Constructors

Quiet	Do not output anything to `stdout`, which most of the time is good.
Verbose	Print what work is being done on each iteraction.
VeryVerbose	Print information about every step, may be useful for troubleshooting.

Instances

Enum Verbose
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods succ :: Verbose -> Verbose # pred :: Verbose -> Verbose # toEnum :: Int -> Verbose # fromEnum :: Verbose -> Int # enumFrom :: Verbose -> [Verbose] # enumFromThen :: Verbose -> Verbose -> [Verbose] # enumFromTo :: Verbose -> Verbose -> [Verbose] # enumFromThenTo :: Verbose -> Verbose -> Verbose -> [Verbose] #
Eq Verbose
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: Verbose -> Verbose -> Bool # (/=) :: Verbose -> Verbose -> Bool #
Ord Verbose
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: Verbose -> Verbose -> Ordering # (<) :: Verbose -> Verbose -> Bool # (<=) :: Verbose -> Verbose -> Bool # (>) :: Verbose -> Verbose -> Bool # (>=) :: Verbose -> Verbose -> Bool # max :: Verbose -> Verbose -> Verbose # min :: Verbose -> Verbose -> Verbose #
Read Verbose
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS Verbose # readList :: ReadS [Verbose] # readPrec :: ReadPrec Verbose # readListPrec :: ReadPrec [Verbose] #
Show Verbose
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> Verbose -> ShowS # show :: Verbose -> String # showList :: [Verbose] -> ShowS #

data LineSearch #

Line search methods that may be used.

Constructors

ApproximateWolfe

Use approximate Wolfe line search.

AutoSwitch Double

Use ordinary Wolfe line search, switch to approximate Wolfe when

|f_{k+1} - f_k| < AWolfeFac * C_k

where C_k is the average size of cost and AWolfeFac is the parameter to this constructor.

Instances

Eq LineSearch
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: LineSearch -> LineSearch -> Bool # (/=) :: LineSearch -> LineSearch -> Bool #
Ord LineSearch
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: LineSearch -> LineSearch -> Ordering # (<) :: LineSearch -> LineSearch -> Bool # (<=) :: LineSearch -> LineSearch -> Bool # (>) :: LineSearch -> LineSearch -> Bool # (>=) :: LineSearch -> LineSearch -> Bool # max :: LineSearch -> LineSearch -> LineSearch # min :: LineSearch -> LineSearch -> LineSearch #
Read LineSearch
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS LineSearch # readList :: ReadS [LineSearch] # readPrec :: ReadPrec LineSearch # readListPrec :: ReadPrec [LineSearch] #
Show LineSearch
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> LineSearch -> ShowS # show :: LineSearch -> String # showList :: [LineSearch] -> ShowS #

data StopRules #

Stop rules used to decided when to stop iterating.

Constructors

DefaultStopRule Double

DefaultStopRule stop_fac stops when

|g_k|_infty <= max(grad_tol, |g_0|_infty * stop_fac)

where |g_i|_infty is the maximum absolute component of the gradient at the i-th step.

AlternativeStopRule

AlternativeStopRule stops when

|g_k|_infty <= grad_tol * (1 + |f_k|)

Instances

Eq StopRules
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: StopRules -> StopRules -> Bool # (/=) :: StopRules -> StopRules -> Bool #
Ord StopRules
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: StopRules -> StopRules -> Ordering # (<) :: StopRules -> StopRules -> Bool # (<=) :: StopRules -> StopRules -> Bool # (>) :: StopRules -> StopRules -> Bool # (>=) :: StopRules -> StopRules -> Bool # max :: StopRules -> StopRules -> StopRules # min :: StopRules -> StopRules -> StopRules #
Read StopRules
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS StopRules # readList :: ReadS [StopRules] # readPrec :: ReadPrec StopRules # readListPrec :: ReadPrec [StopRules] #
Show StopRules
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> StopRules -> ShowS # show :: StopRules -> String # showList :: [StopRules] -> ShowS #

data EstimateError #

How to calculate the estimated error in the function value.

Constructors

AbsoluteEpsilon Double	`AbsoluteEpsilon eps` estimates the error as `eps`.
RelativeEpsilon Double	`RelativeEpsilon eps` estimates the error as `eps * C_k`.

Instances

Eq EstimateError
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: EstimateError -> EstimateError -> Bool # (/=) :: EstimateError -> EstimateError -> Bool #
Ord EstimateError
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: EstimateError -> EstimateError -> Ordering # (<) :: EstimateError -> EstimateError -> Bool # (<=) :: EstimateError -> EstimateError -> Bool # (>) :: EstimateError -> EstimateError -> Bool # (>=) :: EstimateError -> EstimateError -> Bool # max :: EstimateError -> EstimateError -> EstimateError # min :: EstimateError -> EstimateError -> EstimateError #
Read EstimateError
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS EstimateError # readList :: ReadS [EstimateError] # readPrec :: ReadPrec EstimateError # readListPrec :: ReadPrec [EstimateError] #
Show EstimateError
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> EstimateError -> ShowS # show :: EstimateError -> String # showList :: [EstimateError] -> ShowS #

Technical parameters

data TechParameters #

Technical parameters which you probably should not touch. You should read the papers of CG_DESCENT to understand how you can tune these parameters.

Constructors

TechParameters

Fields

techDelta :: Double
Wolfe line search parameter. Defaults to 0.1.
techSigma :: Double
Wolfe line search parameter. Defaults to 0.9.
techGamma :: Double
Decay factor for bracket interval width. Defaults to 0.66.
techRho :: Double
Growth factor when searching for initial bracketing interval. Defaults to 5.
techEta :: Double
Lower bound for the conjugate gradient update parameter beta_k is techEta * ||d||_2. Defaults to 0.01.
techPsi0 :: Double
Factor used in starting guess for iteration 1. Defaults to 0.01.
techPsi1 :: Double
In performing a QuadStep, we evaluate the function at psi1 * previous step. Defaults to 0.1.
techPsi2 :: Double
When starting a new CG iteration, our initial guess for the line search stepsize is psi2 * previous step. Defaults to 2.

Instances

Eq TechParameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods (==) :: TechParameters -> TechParameters -> Bool # (/=) :: TechParameters -> TechParameters -> Bool #
Ord TechParameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods compare :: TechParameters -> TechParameters -> Ordering # (<) :: TechParameters -> TechParameters -> Bool # (<=) :: TechParameters -> TechParameters -> Bool # (>) :: TechParameters -> TechParameters -> Bool # (>=) :: TechParameters -> TechParameters -> Bool # max :: TechParameters -> TechParameters -> TechParameters # min :: TechParameters -> TechParameters -> TechParameters #
Read TechParameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods readsPrec :: Int -> ReadS TechParameters # readList :: ReadS [TechParameters] # readPrec :: ReadPrec TechParameters # readListPrec :: ReadPrec [TechParameters] #
Show TechParameters
Instance details Defined in Numeric.Optimization.Algorithms.HagerZhang05 Methods showsPrec :: Int -> TechParameters -> ShowS # show :: TechParameters -> String # showList :: [TechParameters] -> ShowS #

Re-export

class (Num t, Num (Scalar t)) => Mode t where #

Associated Types

type Scalar t :: Type #

Methods

auto :: Scalar t -> t #

Embed a constant

Instances

Mode Double
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Double :: Type # Methods isKnownConstant :: Double -> Bool # isKnownZero :: Double -> Bool # auto :: Scalar Double -> Double # (^) :: Scalar Double -> Double -> Double # (^) :: Double -> Scalar Double -> Double # (^/) :: Double -> Scalar Double -> Double # zero :: Double #
Mode Float
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Float :: Type # Methods isKnownConstant :: Float -> Bool # isKnownZero :: Float -> Bool # auto :: Scalar Float -> Float # (^) :: Scalar Float -> Float -> Float # (^) :: Float -> Scalar Float -> Float # (^/) :: Float -> Scalar Float -> Float # zero :: Float #
Mode Int
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Int :: Type # Methods isKnownConstant :: Int -> Bool # isKnownZero :: Int -> Bool # auto :: Scalar Int -> Int # (^) :: Scalar Int -> Int -> Int # (^) :: Int -> Scalar Int -> Int # (^/) :: Int -> Scalar Int -> Int # zero :: Int #
Mode Int8
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Int8 :: Type # Methods isKnownConstant :: Int8 -> Bool # isKnownZero :: Int8 -> Bool # auto :: Scalar Int8 -> Int8 # (^) :: Scalar Int8 -> Int8 -> Int8 # (^) :: Int8 -> Scalar Int8 -> Int8 # (^/) :: Int8 -> Scalar Int8 -> Int8 # zero :: Int8 #
Mode Int16
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Int16 :: Type # Methods isKnownConstant :: Int16 -> Bool # isKnownZero :: Int16 -> Bool # auto :: Scalar Int16 -> Int16 # (^) :: Scalar Int16 -> Int16 -> Int16 # (^) :: Int16 -> Scalar Int16 -> Int16 # (^/) :: Int16 -> Scalar Int16 -> Int16 # zero :: Int16 #
Mode Int32
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Int32 :: Type # Methods isKnownConstant :: Int32 -> Bool # isKnownZero :: Int32 -> Bool # auto :: Scalar Int32 -> Int32 # (^) :: Scalar Int32 -> Int32 -> Int32 # (^) :: Int32 -> Scalar Int32 -> Int32 # (^/) :: Int32 -> Scalar Int32 -> Int32 # zero :: Int32 #
Mode Int64
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Int64 :: Type # Methods isKnownConstant :: Int64 -> Bool # isKnownZero :: Int64 -> Bool # auto :: Scalar Int64 -> Int64 # (^) :: Scalar Int64 -> Int64 -> Int64 # (^) :: Int64 -> Scalar Int64 -> Int64 # (^/) :: Int64 -> Scalar Int64 -> Int64 # zero :: Int64 #
Mode Integer
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Integer :: Type # Methods isKnownConstant :: Integer -> Bool # isKnownZero :: Integer -> Bool # auto :: Scalar Integer -> Integer # (^) :: Scalar Integer -> Integer -> Integer # (^) :: Integer -> Scalar Integer -> Integer # (^/) :: Integer -> Scalar Integer -> Integer # zero :: Integer #
Mode Natural
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Natural :: Type # Methods isKnownConstant :: Natural -> Bool # isKnownZero :: Natural -> Bool # auto :: Scalar Natural -> Natural # (^) :: Scalar Natural -> Natural -> Natural # (^) :: Natural -> Scalar Natural -> Natural # (^/) :: Natural -> Scalar Natural -> Natural # zero :: Natural #
Mode Word
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Word :: Type # Methods isKnownConstant :: Word -> Bool # isKnownZero :: Word -> Bool # auto :: Scalar Word -> Word # (^) :: Scalar Word -> Word -> Word # (^) :: Word -> Scalar Word -> Word # (^/) :: Word -> Scalar Word -> Word # zero :: Word #
Mode Word8
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Word8 :: Type # Methods isKnownConstant :: Word8 -> Bool # isKnownZero :: Word8 -> Bool # auto :: Scalar Word8 -> Word8 # (^) :: Scalar Word8 -> Word8 -> Word8 # (^) :: Word8 -> Scalar Word8 -> Word8 # (^/) :: Word8 -> Scalar Word8 -> Word8 # zero :: Word8 #
Mode Word16
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Word16 :: Type # Methods isKnownConstant :: Word16 -> Bool # isKnownZero :: Word16 -> Bool # auto :: Scalar Word16 -> Word16 # (^) :: Scalar Word16 -> Word16 -> Word16 # (^) :: Word16 -> Scalar Word16 -> Word16 # (^/) :: Word16 -> Scalar Word16 -> Word16 # zero :: Word16 #
Mode Word32
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Word32 :: Type # Methods isKnownConstant :: Word32 -> Bool # isKnownZero :: Word32 -> Bool # auto :: Scalar Word32 -> Word32 # (^) :: Scalar Word32 -> Word32 -> Word32 # (^) :: Word32 -> Scalar Word32 -> Word32 # (^/) :: Word32 -> Scalar Word32 -> Word32 # zero :: Word32 #
Mode Word64
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar Word64 :: Type # Methods isKnownConstant :: Word64 -> Bool # isKnownZero :: Word64 -> Bool # auto :: Scalar Word64 -> Word64 # (^) :: Scalar Word64 -> Word64 -> Word64 # (^) :: Word64 -> Scalar Word64 -> Word64 # (^/) :: Word64 -> Scalar Word64 -> Word64 # zero :: Word64 #
Integral a => Mode (Ratio a)
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar (Ratio a) :: Type # Methods isKnownConstant :: Ratio a -> Bool # isKnownZero :: Ratio a -> Bool # auto :: Scalar (Ratio a) -> Ratio a # (^) :: Scalar (Ratio a) -> Ratio a -> Ratio a # (^) :: Ratio a -> Scalar (Ratio a) -> Ratio a # (^/) :: Ratio a -> Scalar (Ratio a) -> Ratio a # zero :: Ratio a #
Num a => Mode (Forward a)
Instance details Defined in Numeric.AD.Internal.Forward Associated Types type Scalar (Forward a) :: Type # Methods isKnownConstant :: Forward a -> Bool # isKnownZero :: Forward a -> Bool # auto :: Scalar (Forward a) -> Forward a # (^) :: Scalar (Forward a) -> Forward a -> Forward a # (^) :: Forward a -> Scalar (Forward a) -> Forward a # (^/) :: Forward a -> Scalar (Forward a) -> Forward a # zero :: Forward a #
Num a => Mode (Kahn a)
Instance details Defined in Numeric.AD.Internal.Kahn Associated Types type Scalar (Kahn a) :: Type # Methods isKnownConstant :: Kahn a -> Bool # isKnownZero :: Kahn a -> Bool # auto :: Scalar (Kahn a) -> Kahn a # (^) :: Scalar (Kahn a) -> Kahn a -> Kahn a # (^) :: Kahn a -> Scalar (Kahn a) -> Kahn a # (^/) :: Kahn a -> Scalar (Kahn a) -> Kahn a # zero :: Kahn a #
Num a => Mode (Sparse a)
Instance details Defined in Numeric.AD.Internal.Sparse Associated Types type Scalar (Sparse a) :: Type # Methods isKnownConstant :: Sparse a -> Bool # isKnownZero :: Sparse a -> Bool # auto :: Scalar (Sparse a) -> Sparse a # (^) :: Scalar (Sparse a) -> Sparse a -> Sparse a # (^) :: Sparse a -> Scalar (Sparse a) -> Sparse a # (^/) :: Sparse a -> Scalar (Sparse a) -> Sparse a # zero :: Sparse a #
Num a => Mode (Tower a)
Instance details Defined in Numeric.AD.Internal.Tower Associated Types type Scalar (Tower a) :: Type # Methods isKnownConstant :: Tower a -> Bool # isKnownZero :: Tower a -> Bool # auto :: Scalar (Tower a) -> Tower a # (^) :: Scalar (Tower a) -> Tower a -> Tower a # (^) :: Tower a -> Scalar (Tower a) -> Tower a # (^/) :: Tower a -> Scalar (Tower a) -> Tower a # zero :: Tower a #
Num a => Mode (Id a)
Instance details Defined in Numeric.AD.Internal.Identity Associated Types type Scalar (Id a) :: Type # Methods isKnownConstant :: Id a -> Bool # isKnownZero :: Id a -> Bool # auto :: Scalar (Id a) -> Id a # (^) :: Scalar (Id a) -> Id a -> Id a # (^) :: Id a -> Scalar (Id a) -> Id a # (^/) :: Id a -> Scalar (Id a) -> Id a # zero :: Id a #
(Mode t, Mode (Scalar t)) => Mode (On t)
Instance details Defined in Numeric.AD.Internal.On Associated Types type Scalar (On t) :: Type # Methods isKnownConstant :: On t -> Bool # isKnownZero :: On t -> Bool # auto :: Scalar (On t) -> On t # (^) :: Scalar (On t) -> On t -> On t # (^) :: On t -> Scalar (On t) -> On t # (^/) :: On t -> Scalar (On t) -> On t # zero :: On t #
RealFloat a => Mode (Complex a)
Instance details Defined in Numeric.AD.Mode Associated Types type Scalar (Complex a) :: Type # Methods isKnownConstant :: Complex a -> Bool # isKnownZero :: Complex a -> Bool # auto :: Scalar (Complex a) -> Complex a # (^) :: Scalar (Complex a) -> Complex a -> Complex a # (^) :: Complex a -> Scalar (Complex a) -> Complex a # (^/) :: Complex a -> Scalar (Complex a) -> Complex a # zero :: Complex a #
(Reifies s Tape, Num a) => Mode (Reverse s a)
Instance details Defined in Numeric.AD.Internal.Reverse Associated Types type Scalar (Reverse s a) :: Type # Methods isKnownConstant :: Reverse s a -> Bool # isKnownZero :: Reverse s a -> Bool # auto :: Scalar (Reverse s a) -> Reverse s a # (^) :: Scalar (Reverse s a) -> Reverse s a -> Reverse s a # (^) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a # (^/) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a # zero :: Reverse s a #
Mode a => Mode (AD s a)
Instance details Defined in Numeric.AD.Internal.Type Associated Types type Scalar (AD s a) :: Type # Methods isKnownConstant :: AD s a -> Bool # isKnownZero :: AD s a -> Bool # auto :: Scalar (AD s a) -> AD s a # (^) :: Scalar (AD s a) -> AD s a -> AD s a # (^) :: AD s a -> Scalar (AD s a) -> AD s a # (^/) :: AD s a -> Scalar (AD s a) -> AD s a # zero :: AD s a #
(Mode a, Mode b, Chosen s, Scalar a ~ Scalar b) => Mode (Or s a b)
Instance details Defined in Numeric.AD.Internal.Or Associated Types type Scalar (Or s a b) :: Type # Methods isKnownConstant :: Or s a b -> Bool # isKnownZero :: Or s a b -> Bool # auto :: Scalar (Or s a b) -> Or s a b # (^) :: Scalar (Or s a b) -> Or s a b -> Or s a b # (^) :: Or s a b -> Scalar (Or s a b) -> Or s a b # (^/) :: Or s a b -> Scalar (Or s a b) -> Or s a b # zero :: Or s a b #